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A260002 Sudan Numbers: a(n)= f(n,n,n) where f is the Sudan function. 5
0, 3, 15569256417 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
The Sudan function is the first discovered not primitive recursive function that is still totally recursive like the well-known three-argument (or two-argument) Ackermann function ack(a,b,c) (or ack(a,b)).
The Sudan function is defined as follows:
f(0,x,y) = x+y;
f(z,x,0) = x;
f(z,x,y) = f(z-1, f(z,x,y-1), f(z,x,y-1)+y).
Just as the three-argument (or two-argument) Ackermann numbers A189896 (or A046859) are defined to be the numbers that are the answer of ack(n,n,n) (or ack(n,n)) for some natural number n, the Sudan numbers are: a(n) = f(n,n,n).
a(3)> 2^(76*2^(76*2^(76*2^(76*2^76)))) so is too big to be included.
LINKS
EXAMPLE
a(1) = f(1,1,1) = f(0, f(1,1,0), f(1,1,0)+1) = f(0, 1, 2) = 1+2 = 3.
MATHEMATICA
f[z_, x_, y_] := f[z, x, y] =
Piecewise[{{x + y, z == 0}, {x,
z > 0 && y == 0}, {f[z - 1, f[z, x, y - 1], f[z, x, y - 1] + y],
z > 0 && y > 0} }];
a[n_] := f[n, n, n]
PROG
(PARI) f(z, x, y)=if(z, if(y, my(t=f(z, x, y-1)); f(z-1, t, t+y), x), x+y)
a(n)=f(n, n, n) \\ Charles R Greathouse IV, Jul 28 2015
CROSSREFS
Sequence in context: A154998 A036236 A235357 * A368723 A058447 A275939
KEYWORD
nonn,bref
AUTHOR
Natan Arie Consigli, Jul 12 2015
STATUS
approved

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Last modified June 22 08:18 EDT 2024. Contains 373567 sequences. (Running on oeis4.)